Any math whizzes out there?

[Little Fishy]

I understand how to calculate strait foreward probablilities but what I'm having trouble with is how to calculate the probabilities of anomolies occuring over the range of a sample:
for instance what is the probability that if you flip a coin 10 times you will get twice as many heads as tails? what if you flip it 100 times or 1,000 times?
Or what is the probability that in hold'em out of a sample of 1,000 hands i get dealt 10% more pocket paris than I "should" given normal distribution?

-little fishy

[The Legend]

for the coin flip thing, lets say you want to have exactly x heads in y flips. This is a binomial distribution, which means the probability is (assuming the probability of heads is p) (y!/(x!*(y-x)!)*(p)^(x)*(1-p)^(y-x). So , for your example, probability of 2x heads then tails ( ill assume 7 heads and 3 tails) is (10!/(7!*3!))*(.5)^7 *(.5)^3

For your pocket pair example, the probability of getting a pocket pair is 13/221(off the top of my head). So, the expected number of pocket pairs would be (13/221)*1000(I wish I had a calculator on me but I don't...). Multiply that by 1.10 to get 10% more. Round that to the nearest whole number, and plug that number in the above equation as x. y is 1000. p is 13/221. Cool for 1-2 minutes before serving.